Question

Using sketchpad, construct the regular tilings for n = 3, for n = 4, and for n = 6.

Answer 1

A tiling refers to any pattern that covers a flat surface, like a painting on a canvas, using non-overlapping repetitions. Another word for a tiling is a tessellation.

The angle should be related to the number of sides. We want to think of the polygon as having a generic number of sides 'n' where 'n' can be 3, 4, 5 ,..... We can find a formula for the angle in terms of the number of sides, here is how.

Let n = number of sides of our regular polygon.

and a = the angle of of our polygon.

    where n = 3 , 4 , 6

Therefore,

For n = 3

For n = 4

For n = 6